Question: The line $y = \frac{3}{2} x - 25$ is parameterized by $(x,y) = (f(t),15t - 7).$  Enter the function $f(t).$
Answer: Let $y = 15t - 7.$  Then
\[15t - 7 = \frac{3}{2} x - 25.\]Solving for $x,$ we find $x = \boxed{10t + 12}.$